I look at it this way, it's 3am you wake up and all of a sudden want waffles. You stumble around and think crap I forget how to make them so of course you turn to google, but wait the internets down because the router is off. By the time you get the modem/router on you died from hunger.
The summary is yeah it's perfectly fine to leave them running like others mine are running 24/7 as well.
yeah hes right man,i remember with my 3+ year old 4mb modem,if i turned it off overnight and switched it on in the morning it would take a good half hour to connect again
things seems to have got better with the new ones though,if you do have to turn them off for some reason they usualy re-connect within a few seconds so its realy not that bad anymore.
but i still leave mine on,they hardly use any power anyway.